The principal subject of this paper concerns algebro-geometric quasi-periodic solutions
of the whole HS2 hierarchy, of which (REF ) (\(\sigma =1\) ) is just the first of infinitely many members.
Algebro-geometric solution, as an important feature of integrable system,
is a kind of explicit solution closely related to the inverse spectral
theory [1]}, [2]}, [3]}-[4]}. In a degenerated case of the
algebro-geometric solution, the multi-soliton solution and periodic solution
in elliptic function type may be obtained [2]}, [6]}, [7]}.
A systematic approach, proposed by Gesztesy and Holden to construct
algebro-geometric solutions for integrable equations, has been extended to
the whole (1+1) dimensional integrable hierarchy, such as the AKNS hierarchy,
the CH hierarchy, etc. [8]}-[9]}.
Recently, we investigated algebro-geometric solutions for the
modified CH hierarchy and the Degasperis-Procesi hierarchy [10]}, [11]}.
